EFF Offers Awards for Large Composite Numbers 
[Apr. 1st, 200908:34 pm]
Daniel

Inspired by the attention its Cooperative Computing Awards has brought to the power of collaboration to solve difficult mathematics problems, EFF today announced a new award. EFF will offer three increasing rewards of $6, $8, and $12 to the persons or team who, working collaboratively, can discover a worldrecord composite number.
Composite numbers are those which are divisible by some whole number other than themselves and one. Familiar examples include 8, 100, 525, and 4294967296. Notably, all even numbers greater than 2 are composite. Composite numbers have important applications in engineering, scientific research and even finance, where they are often used to measure enormously large values with a high degree of precision. Composite numbers are surprisingly common—indeed, most numbers are composite—but naming extremely large composite numbers can become a daunting task.
However, throughout human history, the largest known composite number has consistently been larger than the largest known prime number. Indeed, this trend is likely to continue. The world’s largest known primes have for some time been Mersenne primes; but to every Mersenne number 2^p1 where p is a prime, there corresponds a larger composite number 2^p1+1.
In 2007, two philosophers competed in an event under the auspices of the Massachusetts Institute of Technology to see who could name the largest number using only an ordinary chalkboard. The winning number, found by Prof. Adam N. Elga, was almost certainly composite.
“Huge composite numbers are all around us, but very few people have ever even tried to name a number larger than a googol,” said EFF Staff Technologist Seth Schoen. “Hopefully this contest will remedy that and maybe even set a few records in the process.”
A proof attributed to the Greek mathematician Euclid shows that there is no largest composite number. Euclid suggests multiplying all known whole numbers together and then failing to add one. The result will be divisible by “lots of stuff,” and hence composite.
EFF’s new awards program was established with funds found under a couch cushion one day here at the EFF office. Prospective claimants will—as with EFF’s Cooperative Computing Awards—need to publish their results in a peerreviewed scientific journal, including rigorous proof that the numbers they are claiming are not prime. The proof must also show that a claimed composite number is larger than Prof. Elga’s 2007 record. EFF also reserves the right to require that claimants explicitly identity at least one specific divisor of a claimed composite number. 

